Correction of the year

…and maybe of all time, at least in quantitative terms. In the New York Times Magazine, 4/10/2016:

An article on March 20 about wave piloting in the Marshall Islands misstated the number of possible paths that could be navigated without instruments among the 34 islands and atolls of the Marshall Islands. It is 561, not a trillion trillion.

A trillion trillion is presumably 10²⁴, and 561 is 5.61 x 10², so the original number was off by a factor of about 1.78 x 10²², which is more than a thousand times greater than the estimated number of grains of sand in all the beaches and deserts of planet earth.

The obligatory screen shot:

I don't know how either the original number or the revised number were calculated. One hypothesis might start with 34!, which is about 2.952328e+38, but that seems too big even for the version of trillion that makes it 10¹⁸ rather than 10¹². And (34^2)/2 is 578, not 561. Ideas?

[h/t John Burke]